This is a versatile instrument. It is basically a long piece of uniform wire, sometimes a few meters in length across which a standard cell (B) is connected. In actual design, the wire is sometimes cut in several pieces placed side by side and connected at the ends by thick metal strip. (Fig. 3.28). In the figure, the wires run from A to C. The small vertical portions are the thick metal strips connecting the various sections of the wire.
A current I flows through the wire which can be varied by a variable resistance (rheostat, R) in the circuit. Since the wire is uniform, the potential difference between A and any point at a distance l from A is
ε φ (l l )
where φ is the potential drop per unit length.
A resistance of R Ω draws current from a potentiometer. The potentiometer has a total resistance R0 Ω A voltage V is supplied to the potentiometer. Derive an expression for the voltage across R when the sliding contact is in the middle of the potentiometer.
Solution: While the slide is in the middle of the potentiometer only half of its resistance (R0 /2) will be between the points A and B. Hence, the total resistance between A and B, say, R1 , will be given by the following expression:
1. Current through a given area of a conductor is the net charge passing per unit time through the area.
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